How do I get more weapon slots?

[Corona Varus]

I currently only have two. I keep swapping weapons in the menu when I ran out of ammo.

[Renfrew]

Progressing story missions, eventually you'll get to ones which give you a weapon slot upgrade (applied automatically)

[chris.ferrantegerard]

You receive two extra weapon slots from Weapon Equip Slot SDUs rewarded from quest. The first extra slot is rewarded from Intelligences of the Artificial Persuasion, the second from Home Sweet Home.